The near-infrared luminosity function of cluster galaxies beyond redshift one

0.45 MB·English

by  V. Strazzullo

Astronomy&Astrophysicsmanuscriptno.KLFsub3˙astroph (cid:13)c ESO2008
February5,2008
The near–infrared luminosity function
⋆
of cluster galaxies beyond redshift one
V.Strazzullo1,2,P.Rosati2,S.A.Stanford3,4,C.Lidman5,M.Nonino6,
R.Demarco7,P.E.Eisenhardt8,S.Ettori9,V.Mainieri10,andS.Toft11
1 DipartimentodiScienzeFisiche,Universita`degliStudidiNapoli“FedericoII”,viaCinthia,I–80126Napoli,Italy
6 2 EuropeanSouthernObservatory,Karl–Scwarzchild–Strasse2,D–85748Garching,Germany
0
3 DepartmentofPhysics,UniversityofCaliforniaatDavis,1ShieldsAvenue,Davis,CA95616,USA
0
4 InstituteofGeophysicsandPlanetaryPhysics,LLNL,Livermore,CA94551,USA
2
5 EuropeanSouthernObservatory,AlonsodeCordova3107,Casilla19001,Santiago,Chile

n 6 InstitutoNazionalediAstrofisica,OsservatorioAstronomicodiTrieste,viaG.B.Tiepolo11,I–34131,Trieste,Italy
a 7 DepartmentofPhysicsandAstronomy,JohnsHopkinsUniversity,3400N.CharlesStr.,Baltimore,MD21218,USA
J
8 JetPropulsionLaboratory,CaliforniaInstituteofTechnology,MC169–327,4800OakGroveDrive,Pasadena,CA91109
9 9 IstitutoNazionalediAstrofisica,OsservatorioAstronomicodiBologna,viaRanzani1,I–40127Bologna,Italy

10 Max–Planck–Institutfu¨rextraterrestrischePhysik,Postfach1319,D–85748Garching,Germany
1
11 DepartmentofAstronomy,YaleUniversity,P.O.Box208101,NewHaven,CT06520–8101,USA
v
5
6 Preprintonlineversion:February5,2008
1
1 ABSTRACT
0
6 Context.
0
Aims.WedeterminedtheK bandluminosityfunction(LF),andinferredthecorrespondingstellarmassfunction,ofclustergalaxiesatredshift
h/ z≃1.2,usingnear–infraredsimagesofthreeX–rayluminousclustersatz=1.11,1.24,1.27.
p Methods.ThecompositeLFwasderiveddowntoM∗+4,bymeansofstatisticalbackgroundsubtraction,andiswelldescribedbyaSchechter
- functionwithK∗ =20.5+0.4andα=−1.0+0.2.UsingavailableX–raymassprofileswedeterminedtheM/Lratiosofthesethreeclusters,which
o s −1 −0.3
tendtobelowerthanthosemeasuredinthelocaluniverse.Finally,fromthe K bandcompositeLFwederivedthestellarmassfunctionof
r s
t clustergalaxies.
s
a Results.Withthesedata,nosignificantdifferencecanbeseenbetweentheclustergalaxiesLFandtheLFoffieldgalaxiesatsimilarredshift.
: Wealsofoundnosignificantevolutionouttoz ≃ 1.2inthebright(<M∗+4)partoftheLFprobedinthisstudy,apartfromabrighteningof
v
≃1.3magofthecharacteristicmagnitudeofthehighredshiftLF.Weconfirm,andextendtohigherredshift,theresultfrompreviousworkthat
i
X theredshiftevolutionofthecharacteristicmagnitudeM∗isconsistentwithpassiveevolutionofastellarpopulationformedatz>2.
Conclusions.Theresultsobtainedinthisworksupportandextendpreviousfindingsthatmostofthestarsinbrightgalaxieswereformedat
r
a highredshift,andthat Ks–bright(M > 1011M⊙)galaxieswerealreadyinplaceatz ≃ 1.2,atleastinthecentralregionsofX–rayluminous
clusters.Togetherwithrecentresultsonthefieldgalaxiesstellarmassfunction,thisimpliesthatmostofthestellarmassisalreadyassembled
inmassivegalaxiesbyz≃1,bothinlowandhighdensityenvironments.
Keywords.galaxies:clusters:individual:RDCSJ1252-2927,RDCSJ0910+5422,RXJ0848+4453-galaxies:evolution-galaxies:formation
-galaxies:luminosityfunction,massfunction-cosmology:observations
1. Introduction
Galaxyclustersareraresystemsforminginthehighestdensity
peaks of large scale structure. In these special regionsgalaxy
Send offprint requests to: V. Strazzullo, [email protected], straz-
formationandevolutionaryprocessesareexpectedtobefaster
[email protected]
withrespecttothelowdensityfields,thusmakinggalaxyclus-
⋆ BasedinpartonobservationsobtainedattheEuropeanSouthern
tersabiasedenvironment.Ontheotherhand,clustersofgalax-
Observatory using the ESO Very Large Telescope on Cerro Paranal
ies,particularlyathighredshift(z ≃ 1),provideaveryconve-
(ESOprogram166.A-0701).Basedinpartonobservationsobtainedat
theHaleTelescope,PalomarObservatory,aspartofacontinuingcol- nientplaceforstudyingtheevolutionofmassivegalaxies.Not
laborationbetweentheCaliforniaInstituteofTechnology,NASA/JPL, only do they contain high numbersof such objects, but these
andCornellUniversity. objects turn out to be so evolved (already at z ≃ 1) that they
2 V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone
show a colour–magnitude sequence as clear as at lower red- redshift, so that at least in some cases merging could be re-
shifts. Thus evolved galaxies in distant clusters can be easily quiredtomakethemevolveintolocalBCGs(see forinstance
identifiedevenwithoutcompletespectroscopicfollow–up. Ellis&Jones (2004)). Even if it is difficult to trace a com-
The study of massive galaxies has a relevant role in con- mon“BCGevolutionarypath”,duetotheintrinsicallypeculiar
straining galaxy formation and evolution models, as different nature of these galaxies, some high redshift clusters (includ-
modelsprovidedifferentpredictionsfortheirassembly(inpar- ing Cl1252 (Rosati 2004, Blakesleeetal. 2003) and Cl0848
ticular in the redshiftrange [0÷1]).They couldhave rapidly (vanDokkumetal. 2001)) show signs of interactions or clear
formedtheirstarsathighredshiftandatthesametimeassem- ongoing merging between few massive galaxies which could
bled their stellar mass, and then simply evolved passively as leadtotheformationofacD.
theirstarsaged.Alternatively,massivegalaxiescouldhaveas- However,even if the bulk of the stars had similar ages in
sembledonalongertimescaleinaprocessofcontinuousmerg- the two formation scenarios (i.e. star formation occurring at
ingofsmallerunitsuntilredshift<1.Comparisonofthesedif- the same early epoch in both), the epoch of assembly of the
ferentscenarioshasproventobeadifficulttask:evenifmerg- final mass observedlocally in massive galaxiesis differentin
inggalaxiesareobserved,therelevanceofthemergingprocess thetwocases.Ifmergingisarelevantprocessinthelook–back
in galaxy evolution and especially the epoch at which major time range that we can probe with our observations, looking
mergersoccurisstilldebated. at progressivelyhigherredshiftone shouldsee the numberof
Coloursandspectraofmassivegalaxiesatz ≃ 1showthat massiveobjectsdecreasingastheybreakupintotheirprogen-
thereisasignificantpopulationofsuchsystemsalreadyhosting itors; this would cause an evolution in the shape of the mass
mainlyevolvedstellarpopulations,bothinthefield(seebelow) functionofgalaxies.
andinclusters(Stanfordetal.(19971998),vanDokkumetal. Thedifferencesinthepredictionsofthetwoformationsce-
(1998), Ben´ıtezetal. (1999), DeProprisetal. (1999), narios have recently become less extreme, partly due to the
Rosatietal. (1999), Stanfordetal. (2002), Blakesleeetal. higher redshift peak of the merging activity in ΛCDM mod-
(2003),vanDokkum&Stanford(2003),Kodamaetal.(2004), elsascomparedtostandardCDMinitiallyconsidered,butalso
Lidmanetal. (2004), DeLuciaetal. (2004), Holdenetal. todifferentad–hocrecipesforthestarformationadoptedinthe
(2005ab), Tanakaetal. (2005)). In such studies, the presence hierarchicalmergingmodels.
of evolved stellar populations is generally inferred from It has recently become more evident that, both
fundamental plane or colour–magnitude sequence evolution. in clusters (references mentioned above) and in the
Thesestudiesindicatethatmostofthestarsinmassivegalaxies field (Glazebrooketal. (2004), McCarthyetal. (2004),
wereformedatz > 2.Atthesametimeseveralofthempoint Fontanaetal. (2004), Saraccoetal. (2004), Cimattietal.
out that the less massive the galaxy is, the more likely is the (2002), Franxetal. (2003)), a significant population of mas-
presenceofayoungercomponentinitsstellarpopulation–the sivegalaxiesisalreadyinplaceatz≃1÷2.However,seealso
socalled“downsizing”(Cowieetal.1996)ingalaxieshosting vanDokkum (2005), finding that a considerable fraction of a
starformation. nearby bulge–dominatedgalaxy sample, recently experienced
Itisnotpossible,however,onthebasisofspectrophotomet- a mergingepisodeinvolvingmorethan20%of itsfinalmass.
ricanalysisonly,toruleoutthepossibilitythatthesegalaxies Thestellarmassfunctionofbrightgalaxiesshowsonlyamild
formed via merging of smaller galaxies with already evolved evolution up to redshift 1 , close to the prediction of simple
stellar populations even a short time before being observed. pureluminosityevolution(e.g.Fontanaetal.2004).
For instance, a passively evolving zero–point of the colour– The comparisonwith recentsemi–analyticalmodelshow-
magnitude relation does not imply that the galaxies formed evershowsthatdifferentrenditionspredictverydifferentevo-
longago,butthatthestarsinthegalaxiesformedathighred- lution, especially at higher redshift (i.e. results are very sen-
shift,possiblyinsmallerprogenitors. sitive to the chosen model ingredients), and most of them
In other words, while the underlying stellar populations under–produceverymassivegalaxies(moreseverelythehigher
can place constraints on the details of the star-formation his- the redshift) even when reproducingthe stellar mass function
tory,theycannottellwhenagalaxyassembled.Infact,evenif aroundM∗–however,seealsorecentresultsfromBoweretal.
thesemassivegalaxiesappeartobepassivelyevolving,several (2005). At the same time, Nagamineetal. (2005) show that
studies have noted that to some extent they can still be form- with recent hydrodynamicalsimulations they can account for
ing (or recently have formed) stars (for instance Nakataetal. ≃ 70%ofthetotalstellarmassatz = 0alreadybeingformed
(2001),vanDokkum&Stanford(2003),Holdenetal.(2005c), byz=1.
Demarcoetal.(2005),Jørgensenetal.(2005)),likelyimplying Sinceadirectmeasureofthemassfunctionistoodifficult
merging(asobservedforinstancebyvanDokkumetal.(1999) at high redshift for a reasonably large galaxy sample includ-
andTranetal. (2005)) oranywaysubsequentepisodesof star ingfaintobjects,thenear–infraredgalaxyluminosityfunction
formation.Suchsecondaryepisodesofstarformationareprob- (LF)representsanusefulcheapersurrogate.ThegalaxyLFisa
ably correlated to cluster–relatedprocesses (accretionof field firstorderdescriptionofagalaxypopulation(densityofgalax-
galaxiesorgroupsand clustermerging),since galaxieswhich ies as a function of their luminosity).Despite (or because of)
exhibit these features are often located outside of the clus- its conceptualsimplicity the LF has been for many years one
ter core, or in regions of lower X–ray luminosity. Moreover, ofthemostpopulartoolsfortheinterpretationofgalaxyobser-
the redshiftevolutionof thebrightestcluster galaxies(BCGs) vationsatallredshiftsandinverydifferentenvironments.The
is peculiar and exhibits a large scatter at increasingly high comparisonoftheLFatdifferentredshiftsconstrainsmodelsof
V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone 3
galaxyformationandevolution(Kauffmann&Charlot1998b), We used a K band image of the Cl1252 field obtained
s
while thecomparisonoftheLFin low andhighdensityenvi- with the ISAAC infrared imager at the VLT (Lidmanetal.
ronmentsprobestherelevanceoftheenvironmentaleffectson 2004), a K band image of the Cl0910 field obtained with
s
the galaxy populations. The LF is historically best studied in the Prime–Focus Infrared Camera at the Palomar 5m tele-
richclustersofgalaxies,whichprovidelargenumbersofgalax- scope (Stanfordetal. 2002), and a F160W (≃ H band) im-
iesatthesamedistanceand,atlowredshift,withhighcontrast age of the Cl0848 field obtained with the NICMOS Camera
againstthe background,allowing an efficient identification of 3 on the Hubble Space Telescope. While the quality of the
cluster members with small contamination from background two images for Cl1252 and Cl0848 is excellent (the PSF has
galaxies.Athigherredshift,thefaintluminositiesandthesub- FWHM≃ 0′.′45and0′.′22respectively,withlimitingABmag-
stantialbackgroundcontaminationmakestheLFdetermination nitude ≈ 25), the Cl0910 image has relatively poorer quality
moreuncertain.However,the steadily increasingdata quality, (FWHM ≃ 0′.′9). While for both Cl1252 and Cl0910 the im-
andthequestforstrictconstraintsongalaxyevolutionarymod- ageeffectivelyusedhasaradius≃65”(i.e.slightlymorethan
els,havemadethestudyoftheLFsinhighredshiftclustersand 500kpcinlinearscale),theNICMOSimageforCl0848isrel-
fieldsapopulartopic. ativelysmall(themaximumradiusofthemosaicis≃55”,i.e.
Inthiswork,wedeterminetheLFofdistant(z>1)cluster ≃ 450 kpc at z=1.27). For all the images a catalog was pro-
galaxies in the near–infrared (NIR). NIR galaxy samples are duced with the SExtractor software (Bertin&Arnouts 1996),
particularly well suited for studying galaxy evolution. Apart and MAG AUTO was used as a measure of the total magni-
from advantages such as the smaller effect of dust extinction tude.
(ascomparedtobluerwavelengths),andthek–correctionsrel-
As discussed later, the galaxy luminosity function for all
atively insensitive to galaxy type, they provide a relatively
three clusters was determinedby means of statistical subtrac-
good estimate of the stellar mass in galaxies up to redshift
tion ofthe fore–andbackground(hereafterbackground)con-
z ∼ 2.Therefore,near–infraredluminosityfunctionscantrace
tribution.Since the images are too small to estimate the local
thestellarmassfunctionmoreeffectivelythanbluerbandLFs,
background from the images themselves, a control field was
whicharemoresensitive tothe star formationhistoriesofthe
selected for each of the cluster fields in order to determine
galaxies.
the backgroundcontributionto the galaxycounts.Ideally,the
WhileLFsforclustergalaxiesatlowredshift(z≤0.2÷0.3)
controlfield shouldbeobservedinthesame filterandin very
havebeendeterminedforalargenumberofclusters,allowing
similarconditionsanddepths.ForCl1252thecontrolfieldhas
detailed discussion of the features and the separate contribu-
beenchosenintheFIRES(FaintInfraredExtragalacticSurvey,
tions of differentgalaxypopulationsdown to very faint mag-
Franxetal.(2000),Labbe´etal.(2003))fieldintheHDF–Sre-
nitudes,thedeterminationoftheLFwithcomparableaccuracy
gion, imaged with the same instrument and in the same filter
athighredshiftisclearlymoredifficult.
as the cluster field. Because of its small area, we have com-
The NIR LF of cluster galaxies at high redshift
plemented this field at bright magnitudes with a field in the
(z ≥ 0.8) has been measured by Trentham&Mobasher
GOODS–Sregion,alsoobservedwithVLT/ISAAC(Vandame
(1998), DeProprisetal. (1999), Nakataetal. (2001),
et al, in preparation).For Cl0848the referencefield has been
Kodama&Bower (2003), Toftetal. (2003), Ellis&Jones
takenintheHubbleUltraDeepField(Thompsonetal.2005),
(2004),andToftetal.(2004).Theevolutionofthecharacteris-
alsoimagedwiththesameinstrumentandinthesamefilteras
ticmagnitude M∗ wasfirststudiedbyDeProprisetal.(1999)
theCl0848field.ForCl0910wehadnocontrolfieldavailable
from low redshift up to z ≃ 0.9, finding that it is consistent
imaged with the same instrument, we then selected the refer-
with pure luminosity evolution of a stellar populationformed
ence field in the GOODS–S Ks images observed with both
atz > 2;thisresulthasbeenconfirmedbysubsequentstudies.
NTT/SOFI and VLT/ISAAC. Due to the similarity of the K
The evolution of the faint–end slope was only studied by s
band filters used for the GOODS and Cl0910 images, we ex-
Toftetal. (2003) and Toftetal. (2004), who found a flatter
pect the backgroundestimate to be appropriate. In particular,
slopeathigherredshiftcomparedtothelocalvalue.
theSOFIimagehascomparableseeing(≃ 0′.′9)andcompara-
The adopted cosmology in this paper is H = 70 km
0 blecompletenessmagnitude(seefigure1),andhasthefurther
s−1 Mpc−1, ΩM = 0.3, ΩΛ = 0.7 unless otherwise stated. advantageofbeingwider(smallerPoissonianerrors).
MagnitudesareintheABsystem.
Forthepurposeofidentifyingpoint–likesourceswemade
useoftheHST/ACSimagesavailableforalltheclusterfields
2. Data
(Blakesleeetal. 2003, Postmanetal. 2005) and for the refer-
This work is mainly based on near–infrared images of enceregionsinGOODS–S(Giavaliscoetal.2004)andHUDF
three distant galaxy clusters: RDCS J1252.9-2927 at z = (Beckwith et al., in preparation),and of the HST/WFPC2 for
1.24(hereafterCl1252,Rosatietal. (2004)), RX J0848+4453 thereferenceregionintheHDF–Sfield(Williamsetal.2000).
at z = 1.27 (hereafter Cl0848, Stanfordetal. (1997)), Inallcatalogs,wheneverpossiblethepoint–likesourceswere
and RDCSJ0910+5422 at z = 1.11 (hereafter Cl0910, removedbased on the MAG AUTO vs. FLUX RADIUS plot
Stanfordetal.(2002)).Themainpropertiesofthesethreeclus- derived from the ACS images. The removed sources have
ters are listed in table 1. As the data used in this work have FWHM close to the PSF of the image. Point–like sources in
alreadybeenpublished,wereferthereadertothepaperslisted regions not covered by the ACS image were identified in the
intable2fordetails. SOFI image itself. Since point–like sources are a small frac-
4 V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone
Table1.Mainpropertiesoftheclustersample.DataarefromEttorietal.(2004).
Cluster z T R L M
gas 500 bol tot
keV kpc 1044ergs−1 1014M⊙
RDCSJ0910+5422 1.106 6.6+1.7 818±150 2.83±0.35 4.91±2.93
−1.3
RDCSJ1252.9-2927 1.237 5.2+0.7 532±40 5.99±1.10 1.59±0.35
−0.7
RXJ0848+4453 1.273 2.9+0.8 499±115 1.04±0.73 1.37±0.98
−0.8
Table2.SummaryoftheprincipalcharacteristicsoftheNIRimagesusedforthedeterminationoftheLF.Area istheareaof
eff
theregionactuallyusedinthiswork.
Cluster Telescope/Instrument Filter resolution completeness Area references
eff
′.′ ABmag arcmin2/Mpc2
RDCSJ0910+5422 Palomar5m/PFIC K 0′.′9 21.5 4.35/1.06 Stanfordetal.(2002)
s
RDCSJ1252.9-2927 VLT/ISAAC K 0′.′45 24.5 3.69/0.93 Rosatietal.(2004)
s
Lidmanetal.(2004)
Demarcoetal.(inprep.)
RXJ0848+4453 HST/NICMOS F160W 0′.′22 25 1.84/0.47 Stanfordetal.(1997)
Holdenetal.(2004)
vanDokkum&Stanford(2003)
tionofthetotalcounts,uncertaintiesintheirremovalhavelittle tometry in several passbands, and on the assumption that the
effectonourresults. photometricredshiftqualityremainsthesame forspectralen-
In order to estimate the luminosity function down to the ergy distributions (SED) for which no spectroscopic redshift
faintestmagnitudeallowedbythedata,thereferencefieldhas canbemeasured.
to be complete at least down to the completeness magnitude
Only one (Cl1252) of the three clusters studied has such
of the cluster field. In figure 1 we plot the number counts in
adeepandwidephotometriccoverage(inadditionto38spec-
theclusterandreferencefields(normalizedtotheclusterfield
troscopicallyconfirmedmembers),thatclustermembershipde-
area).Inallcasesthecompletenessmagnitudeofthereference
terminationfullybasedonphotometricredshiftsisfeasible;the
field is fainter or similar to that of the cluster field, therefore
LFforCl1252wasdeterminedinthiswaybyToftetal.(2004)
the following analysis is based on the cluster and reference
(hereafterT04).Sincefortheothertwoclustersstatisticalsub-
fields catalogs down to the cluster field completeness magni-
tractionisatpresenttheonlyviableapproach,theLFofCl1252
tude,withoutcompletenesscorrections.Fromtheturn–overof
was re–determinedwith thismethod,in the same regionasin
the number counts for objects with S/N ratio > 5, the com-
T04,asafirst–ordervalidationofthestatisticalsubtractionpro-
pletenessmagnitudeoftheclusterfieldsisestimatedtobeK
s cedureinthisredshiftrange.
=24.5forCl1252,K =21.5forCl0910,andF160W=25for
s
Cl0848.
This work also makes use of the extensive spectroscopic 3.1. LF determination
campaigns in these three clusters. We refer to Stanfordetal.
(19972002),vanDokkum&Stanford(2003)andDemarcoet ForeachclustertheLFwasdeterminedasfollows.Thegalaxy
al. (in preparation)for details on the spectroscopicfollow–up counts in both the cluster and reference fields were binned,
observations. andthebackgroundcontributionwasestimatedineachbinas
the reference field counts normalized to the cluster area. For
eachbin,theerrorisestimatedasthesuminquadratureofthe
3. Luminosityfunctions Poissonianerrors1+(N+0.75)1/2(Gehrels1986)onbothclus-
terandfieldcountsinthatbin.
Foreachoftheclusterstheluminosityfunction(LF)wascalcu-
latedbymeansofstatisticalsubtraction,i.e. usinga reference The error on the backgroundcounts should also take into
fieldtoremovethebackgroundcontributionintheassumption accounttheeffectsofgalaxyclusteringandofthelensingmag-
that the field galaxy density is constant all over the sky. The nificationofgalaxiesbeyondthecluster.However,anestimate
statistical subtraction of the field galaxies is often considered of the galaxyclusteringcontributionto the numbercountser-
tobeanuncertainmethodofbackgroundremovalespeciallyat roraccordingtotheprescriptionsofHuangetal.(1997)yields
highredshifts,wherethesignaloftheclusteragainsttheback- anegligibledifferencewithrespecttothesimplePoissonianer-
groundisprogressivelylower.However,whileobtainingspec- ror.Sinceasignificantfractionoftheobservedgalaxiesarein
troscopicredshiftsforallclustergalaxiesdowntoareasonably theforegroundoftheclustertheeffectduetolensingislikely
faint magnitude is clearly unfeasible, even the determination small.DuetothelargePoissonianerrorswehave,wecanne-
ofphotometricredshiftsreliesontheavailabilityofdeeppho- glecttheseeffects.
V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone 5
Theexistingspectroscopicdataweretakenintoaccount,so
thatineachbinthebackgroundcontributioncontainedatleast
asmanygalaxiesasthespectroscopicinterlopers,andtheback-
ground corrected counts were at least equal to the number of
confirmedmembers.Thisallowsamoresecuredetermination
oftheLFinthebrightend,whereduetolowcounts(bothinthe
clusterandinthecontrolfields)thestatisticalsubtractionmay
bepoor.IntheareaselectedfortheLFdetermination,mostof
thebrightgalaxieshavemeasuredredshifts:almost80%ofthe
galaxiesdowntoKs=21forCl1252,morethan80%downto
Ks=21forCl0910,andmorethan85%downtoF160W=22
forCl0848.
Since the FIRESfield isquite small, in orderto achievea
betterbackgroundevaluation(andsmallererrors)inthebright
end,thebackgroundestimateforCl1252fromtheFIRESfield
was supplemented with the estimate from the control field in
GOODS–S(ISAAC)formagnitudesbrighterthan21.5.
Due to the lower quality of the Cl0910 K image (seeing
s
≃ 0′.′9), special care was taken for blended objects, particu-
larlyintheoverdenseclusterenvironment.Thankstotheavail-
abilityofHST/ACSimagesinpassbandsF775WandF850LP,
it was possible to crosscheck the catalogs to identify obvious
blendings.Eightcasesofevidentblendingwereidentified:for
six of them, a more ’aggressive’ SExtractor configuration al-
lowedtheblendedsourcetobesplitinsourceslocatedasinthe
ACS images. For the remaining 2 cases no deblending could
be achieved,andas a zero–orderapproximationtheflux from
the sourcewas split accordingto the flux ratioof the blended
sourcesintheHST/ACSF850LPimage.
Theluminosityfunctionsareshowninfigure2.Thebinned
LFs were fit with the usual Schechter (1976) function with a
maximum likelihood method using the Cash (1979) statistics
C = −2Σ[n ln(m) − m− ln(n!)], where n and m are the
i i i i i i i
observednumberofgalaxiesinthe ith magnitudebin,andthe
number of galaxies predicted in the same bin by a Schechter
functionofparametersM∗andα,respectively.Thebest–fitM∗
andαaretheparametersthatminimizeC.Φ∗wasnottakenas
afreeparameter,butwascalculatedforeachchoiceofM∗ and
αbyrequiringthatthetotalnumberofpredictedgalaxiesequal
thenumberofthoseactuallyobserved.
Eventhoughthefaintendslopecannotbewellconstrained
(or is completely unconstrained, as in the case of Cl0910),
duetothewellknowncorrelationoftheSchechterparameters,
leavingbothM∗andαfreeallowsabetterevaluationoftheer-
rorsonM∗.Thebest–fitSchechterfunctionsareoverplottedon
the LFs in figure 2. The best fitting Schechter parameters are
Fig.1.NumbercountsofextendedobjectswithS/N>5inthe
listedintable3.
clustersandreferencefields.Upperpanel:thesolidlineshows
The maximumlikelihoodapproachgivesin principlealso
the numbercountsin the Cl1252field (≃ 3.7 square arcmin).
anestimateoftheconfidencelevelsonthebest–fitparameters,
The circles and the dotted line show the counts in the refer-
as if the Cash statistics is defined as above, ∆C is distributed
ence regions selected in the FIRES and GOODS–S fields re-
like∆χ2,thus∆C = 2.3,6.17givesthe1,2–σconfidencelev-
spectively, normalized to the cluster area. The counts in the
elsfortwointerestingparametersM∗andα.However,itshould
GOODS–S field are shown down to the completenessmagni-
benotedthattheCashstatisticsshouldbeappliedtodatawhich
tude(K ≃ 23).Middlepanel:thesolidlineshowsthenumber
s include background, because the background subtracted data
counts in the Cl0910 field (≃ 4.4 square arcmin). The circles
are notPoisson–distributed,while the Cash statistics assumes
and the dotted line show the expected backgroundlevel from
Poissonprobabilities.Evenifwe believethattherelevanceof
referenceregionsselectedintheSOFIandISAACGOODS–S
the 80% spectroscopic completeness on the LF bright end is
fields,respectively.Lowerpanel:thesolidlineshowsthenum-
importantenough to adoptthe previouslydescribed approach
bercountsintheCl0848field(≃1.8squarearcmin),thecircles
showtheexpectedbackgroundlevelbasedontheHubbleUDF.
In all panels, the symbols/lines showing background number
counts have been shifted by ±0.05 mag along the x–axis to
avoidoverlappingerrorbars.
6 V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone
on binned, backgroundsubtracted counts, we note that in our
LFfittingapproachwehidthefactthatthecountsineachbin
haveerrorslargerthanPoissoniandueto thepreviousstatisti-
calbackgroundsubtraction,andthereforewetendtounderes-
timatetheerrorsonM∗andα.Forthisreason,wealsoadopta
maximum likelihood approach on unbinned, not background
subtracted data. Recently Andreonetal. (2005) summarized
theprincipalreasonswhyoneshouldadoptthisapproach,and
proposedamethodtobeappliedwhentheindividualmember-
ship of the galaxies is unknown. When applying this method
we are thus neglectingourredshiftinformation,which means
thatwewillderiveconservativeconfidenceintervals.
For each of the three clusters we applied the method de-
scribedinAndreonetal.(2005),takingasbackgrounddataset
both the control regions in GOODS(ISAAC) and FIRES for
Cl1252, and the control regions in GOODS(SOFI) and UDF
for Cl0910 and Cl0848 respectively.In brief, we assume that
the background number counts can be described by a power
law (we used three parameters), and that the cluster LF is a
Schechterfunction(alsothreeparameters:M∗,α,andΦ∗).We
then find the parameters that at the same time maximize the
likelihoodforthenumbercountsinthecontrolfield(onlyde-
scribed by the power law), and in the cluster field (described
bythepowerlawplustheSchechterfunction).Inallcases,we
first searched the complete 6 parameter space for the global
maximum,and then foundthe maximumlikelihoodon a grid
in the M∗–α plane (i.e. varying only the remaining four pa-
rameters),so thatwe candrawtheconfidencelevelsforthese
twoparameters.Duetoverylowcounts(asdiscussedbelow),
itwasdifficulttomaximizethelikelihoodagainstM∗andαfor
Cl0848. Since the constraints on the Schechter parameters as
determinedwith the first approachare already veryloose, for
thisclusterwequotetheminthefollowing.
In figure 2 we show for reference the 1– and 2–σ confi-
dence levels obtained with the two different approaches for
Cl1252 and Cl0910. As we mentioned, the smaller ones are
understimatedbutthelargeronesarelikelyoverestimated,thus
the‘real’confidencelevelsareexpectedtoliebetweenthetwo.
TheerrorswequoteinthefollowingforCl1252andCl0910are
derivedfromthelargerones.
The Cl1252 LF is shown together with the LF based on
photometricredshiftsfromT04:the twodeterminationsagree
within the errors, with a larger discrepancy for the last mag-
nitudebin.ThedifferencebetweenthetwoLFscouldbecon-
sideredameasureofthesystematicsofthetwomethods,with
theerrorbudgetstilldominatedbylownumberstatistics. The
Fig.2.IndividualclusterluminosityfunctionsforCl1252(up-
slope α determined via statistical subtraction (−0.9± 0.3) is
perpanel),Cl0910(middle),andCl0848(lower).Inallpanels,
somewhatsteeperthantheonedeterminedviaphotometricred-
thesolidlineshowsthebest–fitSchechterfunctionasderived
shifts(α = −0.64+0.27),howeverthetwoestimatesareconsis-
−0.25 fromthebinnedcounts,andtheinsertedplotshowsthe1,2–σ
tentwithintheerrors.TheK∗ value(20.1+1.1)isalsofoundin
s −1.2 confidencelevelsontheparametersM∗andα,calculatedfrom
agreementwiththedeterminationbyT04(K∗ =20.41+0.45).
s −0.55 the maximumlikelihood on binned counts (dashed lines) and
The Cl0910 Schechter function plotted in figure 2 is the
from the maximum likelihood on unbinned, not background
formal best fit with K∗ = 20.4 and α = −0.85. As it is clear
s subtracted counts (solid thick lines – not shown for Cl0848,
fromfigure2,theslopeαisunconstrained.Assuming−1.4 <
see text). The thick and thin crosses show the position of the
α<0.4yieldsanerrorof±1magonK∗.
s best–fit parameters derived with the former and latter meth-
Finally, some caveats apply to the determination of the
ods, respectively (see text for details). In the upper panel the
Cl0848 LF. Namely, i) the very small field of view (less than
emptycirclesshowtheCl1252LFasdeterminedbyT04,and
200 objects brighter than H ≃ 25), resulting in signifi-
F160W the dotted histogram shows for comparison the LF from this
workbinnedwiththesamebinsizeasinT04.
V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone 7
cantPoissonianerrors,ii)thelikelyintrinsicallylowerrichness
ofCl0848comparedtoCl0910andCl1252(sinceCl0848has
lowermass),iii)thepresenceofaknownunderlyingsuperclus-
ter in the Lynx field, and of a lower redshiftcluster projected
in the supercluster region (Stanfordetal. 2001, Nakataetal.
2005). Mainly due to the first two reasons, the constrains on
the Schechter parameters are quite loose, despite the signifi-
cantdepthoftheF160Wimage.Theformalbest–fitSchechter
parametersareF160W∗=20.8+1. andα=−1.15+0.4.
−1.6 −0.3
3.1.1. Compositeluminosityfunction
Summingupthegalaxynumbercountsofdifferentclustersal-
lowsthebackgroundsubtractiontobemoreeffective(averag-
ingoveruncertaintiesinthestatisticalsubtractionineachsin-
gle cluster), and the shot noise to be reduced. The composite
luminosityfunctionwascalculatedintheobservedK bandat
s
z=1.2.ForthisreasontheF160Wmagnitudesatz=1.27were Fig.3. The composite cluster luminosity function at z=1.2
k–correctedtoK magnitudesatz=1.2. (filled dots) compared to the field galaxies LF at z ≃ 1. The
s
Asinglek–correctionof0.5wasappliedatallmagnitudes, solid line shows the best–fit Schechter, and the inserted plot
as derived from synthetic SEDs (Bruzual&Charlot 2003) of shows the 1, 2–σconfidence levels on the Schechter parame-
evolvedsimplestellarpopulationsatthatredshift(3≤age≤5 tersasinfigure2.Allfield galaxiesLFshavebeenarbitrarily
Gyr) No correction was made for the negligible k–correction rescaled.
between z = 1.2 and z = 1.106 or z = 1.237. All the indi-
vidual LFs were binned with a bin size of 0.5 mag (binning
wasadjustedtooptimizeindividualmagnitudecoveragetaking
into accountcompletenesslimits and correctionsfor different
redshift). Cl1252 and Cl0848 have the same “K ” band com-
s
pletenessafterthesecorrections,sotheirLFswerejustsummed
up,andtheerrorswereaddedinquadrature.Cl0910insteadis
much shallower, so its LF was added to the composite LF up
toitscompletenessmagnitude.ThecompositeLFbeyondthis
magnitude is computed as the composite LF without Cl0910
multiplied by the ratio of the total counts (including all three
clusters)tothetotalcountsexcludingCl0910,computedinthe
magnitudeintervalwhere the Cl0910 photometryis complete
(and errors were scaled accordingly). Due to the bright com-
pleteness limit for Cl0910, and the low counts for Cl0848, it
is clear that the faint end of the composite LF is dominated
by Cl1252. In our case, building the composite LF follow-
ing other commonmethods as described in Colless (1989) or
inGarillietal. (1999),producesresultsconsistentwithin1–σ Fig.4. The composite cluster luminosity function at z=1.2
withtheLFcalculatedasabove(notethatthemethoddescribed (filleddots)comparedtothelocalclustergalaxiesLF,corrected
inGarillietal.(1999)tendstogivesmallererrors,andaflatter by1.3magforpassiveevolution(seetext).Thesolidlineshows
slopethantheoneinColless(1989)). the best–fit Schechter, and the inserted plot shows the 1, 2–
ThecompositeLFwasalsoderivedwithamaximumlike- σconfidencelevelsontheSchechterparametersasinfigure2.
lihoodapproachonunbinned,notbackgroundsubtracteddata, AlllocalclustergalaxiesLFshavebeenarbitrarilyrescaled.
as described in Andreonetal. (2005). However, since the LF
of Cl0848 is measured in a different passband than those of
Cl1252andCl0910,Cl0848wasnotincludedinthiscase.The −1.0+0.2. In figure 3 we also show the field LF at z ≃ 1 from
−0.3
composite LF was determined by fitting at the same time the Pozzettietal. (2003), Droryetal. (2003) and Dahlenetal.
countsinthetwoclusterfields(Cl1252andCl0910)andinall (2005). In figure 4 the composite LF is compared to the lo-
the Ks band control fields. The two cluster LFs are assumed cal cluster galaxies K band LF (corrected by 1.3 mag for
to be described by the same M∗ and α (but clearly have two passive evolution as derived below) as measured in Coma
differentΦ∗). by DeProprisetal. (1998) and Andreon&Pello´ (2000), and
The composite luminosity function is shown in figures 3 in samples of nearby clusters by Baloghetal. (2001) and
and 4. The best–fit Schechter has K∗ = 20.5+0.4 and α = Linetal. (2004). All the local and field LFs have been arbi-
s −1
8 V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone
We then built the Cl0910 and Cl1252 LFs as described
above(makinguseofthespectroscopicinformation),basedon
these18smallcontrolfields,andforeachoftheseweredeter-
mined the composite LF. For Cl0848 we always used the LF
determined above, since due to its very large uncertainties it
has lower weight compared to Cl0910 and Cl1252. Thus, we
obtained18 compositeLFs correspondingto differentcontrol
fields.
The GOODS–S ISAAC data, while being considerably
wide,arenotdeepenoughtoreachourfaint–endmagnitudes.
Therefore,wecomplementedthecountsfromeachISAACtile
at magnitudes fainter than its completeness with the FIRES
counts.Inthisway,weprobefield-to-fieldvariationsatmagni-
tudes brighterthan K ≃ 23. The mediansand standarddevi-
s
ationsofM∗ andαobtainedfromthese18determinationsare
Fig.5. The backgroundnumber countsas estimated in differ- M∗=20.5mag,σM∗=0.14mag,α=-1.0,σα =0.06.
entcontrolfields.Thefilledsymbolsshowthecountsfromthe In order to also account for field-to-field variations at
control field in the FIRES region, the solid and dashed lines fainter magnitudes (probed only by FIRES), we repeated the
from those in the GOODS–S regions (ISAAC and SOFI, re- LFs determination by normalizing the FIRES counts at faint
spectively), and the dotted lines show the counts from the 17 magnitudesbytheratiooftheISAAC/FIREScountsatmagni-
ISAACtilesintheGOODS–Sfield. tudesbrighterthanthecompletenessineachtile,assumingthat
thenumberdensityratioisthesameatfaintermagnitudes.The
medians and standard deviations of M∗ and α obtained from
the18redeterminationswiththisprocedureareM∗=20.5mag,
trarily rescaled. Both the Coma LFs shown were measuredin
theHbandandshiftedtoKbandwithacolourtermH−K = σM∗=0.09mag,α=-1.0,σα =0.09.
0.24. The K band field LFs from Pozzettietal. (2003) and Infigure6,weshowtheresultsfromthesetwosetsoftests.
Droryetal.(2003),andtheJbandfieldLFfromDahlenetal. Inthemainpanel,we showtheconfidencelevelsasshownin
(2005), wereconvertedto observedK magnitudesat z = 1.2 figures3and4,andweoverplottheSchechterparametersM∗
s
byequations2and1inPozzettietal.(2003). and α obtained for the 18 LFs. Since most of the data points
With these data, no significant difference can be seen be- overlap near the original determination marked by the cross,
tween the shapesof the cluster and field luminosity functions weshowtheirdistributionsintheside–panels.
intheprobedmagnituderange,evenifwefindsomeevidence
ofanexcessofverybrightgalaxieswithrespecttothefield,as
3.2. Evolutionofthe restframe K bandLF
suggestedforinstanceinDeProprisetal.(2003).
Thederivationofluminosityfunctionsbasedonstatistical ItiscustomarytocomparetheobservedevolutionofM∗ with
subtractionmay be affected by field-to-fieldvariations,as the redshiftwithdifferentpredictions.EvenifinitiallyBargeretal.
backgroundevaluatedfromacontrolfieldmaynotberepresen- (1998) found no significant evolution for the infrared M∗ up
tativeofthebackgroundintheclusterfield.Arobustestimate to z > 0.5, first DeProprisetal. (1999) and then other works
of such an effect requires adequately deep and large K band onhighredshiftclusters(Nakataetal.2001,Kodama&Bower
fields. The VLT/ISAAC observations of the GOODS–S field, 2003, Massarottietal. 2003, Toftetal. 2003, Ellis&Jones
covering ∼ 100arcmin2, are currently the best data set avail- 2004) found that the evolution of M∗ up to z ≃ 1 is con-
able for this purpose.We note that partof this same field has sistent with pure luminosity evolution of the cluster galaxies,
been used as controlfield for determining the LFs of Cl0910 and inconsistent with no–evolution predictions. As discussed
andCl1252.Ineachof17selectedISAACtilesinGOODS–S, in Andreon (2001) and Andreon (2004), measuring an evolu-
we considered all galaxieswithin the central region(with the tion in the LFfroma changein the best–fitSchechterparam-
same area as the Cl1252 field used for the LF), down to the eters is not straightforward. A density (clustercentric radius)
photometriccompleteness.We also consideredin this case as dependent LF would imply a dependence of M∗ (and α) on
an“additionaltile”theFIRESHDF–Sfieldwealreadyusedas the surveyed area in different clusters at different redshifts,
controlfieldforCl1252. and the correlation of M∗ and α could introduce spurious re-
Infigure5,weshowthebackgroundnumbercountsasesti- sults. This makes it difficult to study the LF evolution exclu-
matedfromdifferentcontrolfields:thosefromtheFIRESfield, sively based on the evolution of the characteristic magnitude
whichwasusedascontrolfieldforCl1252(area≃5arcmin2) M∗. However, it is unlikely that the bright end of the LF is
atfaintmagnitudes,thosefromtheISAACGOODS–Smosaic dominatedbygalaxiesintheclusteroutskirts,andeventhough
used to complement the Cl1252 control field at bright mag- the LF has indeed been found to be dependent on the sam-
nitudes(area ≃ 53 arcmin2), those fromthe SOFI GOODS–S pled region within the cluster, this dependencemostly affects
mosaicusedforCl0910(area≃152arcmin2),andthosefrom the LF at magnitudes fainter than those we can probe in this
the17ISAACtilesinGOODS–S(area≃3.7arcmin2each). work(e.g.,Popessoetal. (2005)).WhencomparingLFsfrom
V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone 9
Fig.6. Impactof field-to-fieldvariationson the determination Fig.7. The redshift evolution of the characteristic magnitude
oftheLF.Inthemainpanelthebest–fitM∗ andα(cross)and K∗. Differentsymbolsshow differentdeterminationsof K∗ as
their 1– and 2–σ confidence levels are shown, as in figures 3 indicated in the legend. The no evolution prediction is calcu-
and4.TheM∗ andαparametersfromLFdeterminationswith latedfromtheComaK∗ (DeProprisetal.1998),k–corrected
18 different small control fields are shown as squares. In the as in Pozzettietal. (2003). Passive evolution model predic-
side–panels the distributions of these M∗ (top) and α (right) tions are from Kodama&Arimoto (1997), normalized to the
are shown. Solid symbols (in the main panel) and solid lines ComaK∗.Alldeterminationshavefixedslopeα=-0.9,except
(inthesidepanels)showtheresultsforGOODS–Stilescounts Andreon (2001), Toftetal. (2003), Linetal. (2004), T04 and
complemented with FIRES counts at faint magnitudes, while thepresentwork.ForLinetal.(2004)theplottedvalueisthe
emptysymbolsanddottedlinesshowtheresultswithmodified meanoftwo valuesdeterminedforα = −0.85andα = −1.1.
FIREScountsatfaintmagnitudes(seetextfordetails). ForboththisworkandToftetal.(2003)alsotheK∗valuewith
α fixed at -0.9 is shown (correspondingempty symbol). Note
thaterrorsonM∗whicharecomputedwithαfixedandfreeare
different studies, we note that our LF is based on the central not directly comparable.Errorbars on the x–axis, when plot-
r ≤ 500 kpc cluster regions, approximately correspondingto ted,representtheredshiftrangeofclusterswhicharecombined
r500,whiletheDeProprisetal.(1998)LFisdeterminedinthe todrawthatpoint.
centralr ≤350kpcComaregion,theAndreon&Pello´ (2000)
LFisdeterminedina≃500×500kpc2regionoffsetby≃360
kpcfromthe Comacentre,andtheLinetal. (2004)LFis de- M⊙ (for a Salpeter IMF). For our composite LF this GDR is
terminedwithinthevirialradiusandisfoundtobeverysimilar 0.2±0.1.IfweestimatethisGDRwiththesameabsolutemag-
totheLFderivedwithinr . nitudecutusingtheComaLFsasshowninfigure4(i.e.keep-
500
Finally,ifαisfreeintheSchechterfit,theerrorsonM∗are ingintoaccountthe1.3magbrightening),we similarlyfinda
reliableenoughtomakeafaircomparisonoftheM∗ evolution GDRof0.2−0.3.Thissuggeststhatalargefractionofthegi-
withdifferentpredictions. antpopulationwasalreadyinplaceatz ∼1.Weremindthata
The comparison with previous determinations of K∗ at computationof evolutioncorrections,k–corrections,andH-K
s
lower and similar redshift is shown in figure 7. In agreement colour terms at redshift zero, are involved in such a compar-
withpreviouswork,themeasuredK∗isconsistentwithpassive ison. We also remind that we are applying a single 1.3 mag
s
evolutionpredictionsforanL∗galaxyformedatz≥2. brighteningforthewholeLF, whichisclearlyasimplisticas-
ConvertingtheobservedK∗totheabsoluteK bandmagni- sumption,sincegalaxieswithdifferentstarformationhistories
s s
tudeviaK =K -5log(d /10pc)-(K -K ) ,asin havedifferentevolutioncorrections.
s,rest s,obs L s,rest s,obs z
Pozzettietal.(2003),givesK∗ = −23.41+0.4.Comparedto
s,rest −1
theComaLFK∗ ≃−22.15(DeProprisetal.1998),thisyields
s 3.3. Contributionto the LFfrom earlyandlate type
anevolutionof∆K∗ =−1.3+0.5.Asshowninfigure4,theshape
−1 galaxies
of the composite LF is very similar to the shape of the local
clustergalaxiesLFshifted1.3magnitudesbrighter. ThestudyoftheearlyandlatetypegalaxiesLFsatthisredshift
This shape may be quantified in a non–parametric way ischallenging.
by an analogue of the ‘giant–to–dwarf ratio’ (GDR), which Evenwhen deepACS data are available,(asin the case of
is defined in this case as the ratio of the number of galaxies Cl1252),morphologicalanalysisisnotfeasibleatthefaintend
brighterthanK =21.2tothenumberofgalaxieswith21.2 < (z & 25). Here we use the morphologicalinformation pre-
s AB
K < 24.2. The K = 21.2 threshold corresponds to an abso- sentedby(Blakesleeetal.2003),whichisbasedoniorzband
s s
lutemagnitudeof≃ −22.7,andtoastellarmassof≃ 8×1010 ACS imaging. Due to the red B−z restframe colours (corre-
10 V.Strazzulloetal.:Thenear–infraredluminosityfunctionofclustergalaxiesbeyondredshiftone
spondingapproximatelyto the observedz−K), it is notpossi-
bletobuildamorphologicalcatalogdowntotheK bandcom-
s
pletenessmagnitude.Ontheotherhand,ifearlyandlatetypes
are distinguishedbasedon their colours,while the cluster red
galaxiescanstill beisolated withrelativelysmallbackground
pollution,thisdoesnotholdforthebluepopulation.Forthese
reasonsweonlyattemptaseparationofthecontributionstothe
LF fromearly and late type galaxiesfor the brightend of the
Cl1252LF.
For this cluster we can use the photometric members se-
lected in T04, and distinguish early and late types based on
thebest–fittingtemplatefromphotometricredshifts.Thepho-
tometric redshifts in T04 were determined with 7 passbands
againstfourtemplates(E/S0,Sbc,Scd,Irr)fromColemanetal.
(1980),twostarburstSEDsfromKinneyetal. (1996), andin-
terpolationsbetweenthesesixSEDs(seeT04fordetails).We Fig.8.ThecontributionofearlyandlatetypegalaxiestotheLF
thendefinedasearly–typesthosegalaxiesbestfittedwithSEDs ofCl1252.ThefilledandemptysymbolsshowtheLFsforearly
earlierthanmidwaybetweenE/S0andSbc(i.e.roughlyinclud- and late type photometric members (based on the T04 sam-
ing E/S0 and possibly some Sa galaxies). We can then sepa- ple),classifiedfromtheirbroadbandcolours.Thedashedline
rate the two contributionsto the LF, virtually down to the Ks showsthecontributionofmorphologicallyselectedearly–types
band completeness magnitude, using the completeness func- (Blakesleeetal. 2003). The solid histogram shows the num-
tioncalculatedbyT04(theirfig.5)tocorrectboththeearlyand bercountsofallgalaxies(excludingspectroscopicinterlopers)
late–typesLFsforincompletenessduetophotometricredshifts. alongtheredsequenceasdeterminedin(Blakesleeetal.2003)
Whilethereliabilityofphotometricredshiftsmaybeuncertain (no statistical subtraction of the field galaxies contamination
atthefaintend,theearly/late-typeseparationatthebrightend wasmade;theshadedareashowstheeffectofphotometricer-
isrobustandthecompletenesscorrectionnegligible. rors – see text). The solid curve shows the best–fit Schechter
Infigure8theearly(filleddots)andlate–types(emptycir- functionfortheCl1252globalLF.
cles) brightend LFs are shown, where the separationin early
andlate–typesreflectstheirSEDproperties.Wealsoshowasa
dashedline the LF ofearly typegalaxiesmorphologicallyse-
lected by Blakesleeetal. (2003) (brighterthan K < 22.5, as
s A solid determination of the LF of red-sequence galaxies
thetypicalz-Kcoloursdrivethesamplebeyondthez com-
850 wouldrequireevenmoreextensiveredshiftinformationatthe
pletenesslimitatfaintermagnitudes).Themorphologicallyand
faint end, which is howeverbeyondthe currentspectroscopic
SED–selected early–types LFs are in very good agreement,
limit.Withourdata,weobservesomeevidenceofadeficitof
suggestingthat the brightend of the LF is alreadydominated
faint galaxies on the red–sequence, which has been reported
byearly–typegalaxies,eitherselectedontheirmorphologyor
in other studies (Kajisawaetal. (2000), Nakataetal. (2001),
ontheirspectrophotometricproperties.
Kodamaetal. (2004), DeLuciaetal. (2004), Tanakaetal.
A histogram of the red–sequence galaxies (which are ex- (2005)),andisusuallyinterpretedasasignofdownsizing.
pectedtobemostlyearlytypes)isalsoshownforcomparison
This was derived taking all the galaxies(within 65′.′ from the
cluster center) with i -z colours 0.16 mag redder or 0.14 3.3.1. Contributionfrom clusters to thebright
775 850
magbluerthantheredsequencedeterminedbyBlakesleeetal. galaxiesbudget
(2003). This is much larger than the intrinsic scatter found
Aroughestimateofthecontributionofthebrightclustergalax-
by Blakesleeetal. (2003), however the colours we used are
1′.′5 aperture colours, correspondingly the scatter is expected ies(<M∗ +2)tothetotalbright(<M∗ +2)galaxybudgetcan
beobtained,bycombiningtheclustergalaxiesLF(anditsmea-
to be larger. No statistical subtraction was attempted in this
sured evolution)with the knownspace density of clusters out
case,sinceareferencefieldwithdeepenoughK ,i andz
s 775 850
toz∼1.
imaging is available, however spectroscopic interlopers were
removed. As a result, the histogram shown is an upper limit Our results show that at least at magnitudesbrighter than
to the effectiveLF of red sequencegalaxies. The shadedarea M∗ +2, the cluster galaxies LF appears to evolve mainly by
representsthe16–84percentilevariationsofthishistogramdue passiveevolutionuptoz≃1.Inaddition,thenormalizationof
tophotometricerrors,andwasderivedbysimulating100cat- the K band galaxy LF of X–ray luminous clusters was found
alogswherethei -z colourwasrandomlyshiftedwithina to be consistent with the local one at least out to z ≃ 0.8
775 850
Gaussianofσequaltothephotometricerroronthei -z (Trentham&Mobasher1998).Therefore,we canassumethat
775 850
colour.Thishistogramalso confirmsthattheLFbrightendis high–redshiftclustersofagivenX–rayluminositycontainsim-
largely dominatedby galaxieshosting evolved stellar popula- ilarnumbersofbright(<M∗+2)galaxiesaslow–redshiftclus-
tions. tersofthesameX–rayluminosity.